1. Field of the Invention
The invention relates to a decision feedback equalizer (DFE), and more particularly to a pipelined adaptive decision feedback equalizer (ADFE) that is able to relax the iteration bound in the decision feedback loop (DFL) and maintain signal to noise ration (SNR) equal to that of traditional DFE.
2. Description of the Related Art
Adaptive decision feedback equalizer (ADFE) using the least mean-squared (LMS) algorithm is a well-known equalization technique for magnetic storage and digital communication. The basic block diagram of traditional ADFE is depicted in FIG. 1, where ADFE is composed of two main finite impulse response (FIR) filters, the feedforward filter (FFF) 102 and the feedback filter (FBF) 104. A signal x(n) received from a channel is input to the ADFE. The outputs from both filters are added by an adder 112 and fed into a slicer 106. The signal output from the slicer 106 is the final equalized data. The basic function of the FFF 102 and the FBF 104 is to cancel the pre-cursor and post-cursor inter-symbol interference (ISI) respectively, while the WUC 108 and WUB 110 in the figure stand for the weight-update blocks for the FFF 102 and the FBF 104. Delay units D represent one-tap delay blocks. Delay units D1 and delay units D2 respectively represent n1-tap delay blocks and n2-tap delay blocks. In addition, n1 and n2 are positive integers. A vector of error values e(n) computed as the difference between the output of the slicer 106 and the output of the adder 112 outputs from an adder 114. The vector of error values e(n) is respectively delayed by the delay units D1 and the delay units D2, and then respectively fed back to the WUC 108 and WUB 110 to adapt the tap weights.
Basically, the fine-grain pipelining of the ADFE is known to be a difficult problem for high-speed applications. This is due to the decision feedback loop (DFL). According to the Iteration Bound theory, the smallest clock period of ADFE is bounded by the DFL. Thus, the presence of the above adaptation loop makes it even more difficult to achieve pipelining.
Several approaches are proposed to solve the aforementioned problems. For example, pipelining the ADFE can be achieved by pre-computing all possible in DFL to open the DFL. (See K. K. Parhi, “Pipelining in algorithm with quantizer loops,” IEEE Trans. Circ. Syst., vol. 38, pp. 745-754, July 1991). However, the parallel approach results in large hardware overhead as it transforms a serial algorithm into an equivalent (in the sense of input-output behavior) pipelined algorithm. Another algorithm is proposed in Naresh R. Shanbhag, and Keshab K. Parhi, “Pipelined adaptive DFE architectures using relaxed look-ahead,” IEEE Trans. Signal Processing, vol. 43, No. 6, pp. 1368-1385, June 1995 (hereinafter Naresh et al), which is referred as PIPEADFE2. It maintains the functionality instead of input-output behavior using the technique of relaxed look-ahead.
FIG. 2 is a block diagram illustrating a configuration of the PIPEADFE2 as disclosed in Naresh et al. The PIPEADFE2 is composed of two main FIR filters, the feedforward filter (FFF) 202 and the feedback filter (FBF) 204. A signal x(n) received from a channel is input to the PIPEADFE2 and n is a time instance. The signal x(n) is delayed by a delay unit D, and then input to a pre-processing unit (PP) 220. The PP 220 receives coefficients from the WUB 210. The output of the PP 220 and the signal x(n) are added by an adder 216 and fed into the FFF 202.
In addition, the outputs from the FFF 202 and the FBF 204 are delayed by delay units D1, and then added by an adder 212 and fed into a slicer 206. The signal output from the slicer 206 is the final equalized data. The basic function of the FFF 202 and the FBF 204 is to cancel the pre-cursor and post-cursor ISI respectively, while the WUC 208 and WUB 210 in the figure stand for the weight-update blocks for the FFF 202 and the FBF 204. C(n) is the vector of FFF coefficients and D(n) is the vector of FBF coefficients.
Moreover, delay units D represent one-tap delay blocks. The delay units D1 and delay units D2 respectively represent n1-tap delay blocks and n2-tap delay blocks, where n1 and n2 are positive integers. An error vector e(n) output from an adder 214 defines a vector of error values computed as the difference between the output of the slicer 206 and the output of the adder 212. Then, the error vector e(n) is respectively fed back to the WUC 208 and WUB 210 to adapt the tap weights.
The algorithm used in the PIPEADFE2 is explained as follows.
The channel is assumed as (1+az−1) where the post-curser term is a (a<1), and there is no pre-cursor term. For the traditional ADFE shown in FIG. 1, after the ADFE is converged, the first FBF weight is (−a). The coefficients of the FFF 202 are the inverse transfer function of pre-cursors, but those of the FBF 204 are exactly negative value of post-cursors. However, the datum, to be multiplied by the first weight (−a), is in the DFL, and the circuit will limit the speed.
In PIPEADFE2, the input signal x(n) is filtered by the PP 220, where the transfer function is 1−az−1 (put the coefficient into the PP 220, which can be found in FIG. 6 or Eq. (24b) in Naresh et al). After combining the transfer function of the channel and the PP 220, the effective transfer function combining PP and the channel is (1+az−1)(1−az−1)=1−a2z−2, where the term z−1 disappears. It means the transfer function of FBF 204 is modified from (−a+0z−1) to (0+a2z−1). Thus, the first coefficient can be zero to relax the critical path by a tap of delay. After the cut-set transform, the delay can be moved to the output of FBF 204. Therefore, the algorithm of PP-ADFE can be derived.
Secondly, the channel is considered as (1+az−+bz−2) and the PP 220 is increased to 2 taps. The effective transfer function of the PP 220 and the channel is (1+az−1+bz−2)(1−az−1−bz−2)=1+0z−1−a2z−2−2abz−3−b2z−4. For low pass channel, i.e., 1>a>b, the term (+2abz−3−b2z−4) is very small and the performance is almost the same as traditional ADFE. However, on the other hand, for a specific band pass filter, 1>b>a, the duration of FBF 204 should be extended and the term (−2abz−3−b2z−4) is large enough to degrade the convergence speed.
Therefore, even though the DFL problem can be addressed by PIPEADFE2, the output SNR of PIPEADFE2 is channel dependent and will be degraded in non-lowpass type channels.